Best Known (26, 36, s)-Nets in Base 9
(26, 36, 1314)-Net over F9 — Constructive and digital
Digital (26, 36, 1314)-net over F9, using
- 91 times duplication [i] based on digital (25, 35, 1314)-net over F9, using
- net defined by OOA [i] based on linear OOA(935, 1314, F9, 10, 10) (dual of [(1314, 10), 13105, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(935, 6570, F9, 10) (dual of [6570, 6535, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(935, 6571, F9, 10) (dual of [6571, 6536, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(933, 6561, F9, 10) (dual of [6561, 6528, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(925, 6561, F9, 7) (dual of [6561, 6536, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(935, 6571, F9, 10) (dual of [6571, 6536, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(935, 6570, F9, 10) (dual of [6570, 6535, 11]-code), using
- net defined by OOA [i] based on linear OOA(935, 1314, F9, 10, 10) (dual of [(1314, 10), 13105, 11]-NRT-code), using
(26, 36, 6573)-Net over F9 — Digital
Digital (26, 36, 6573)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(936, 6573, F9, 10) (dual of [6573, 6537, 11]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(935, 6571, F9, 10) (dual of [6571, 6536, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(933, 6561, F9, 10) (dual of [6561, 6528, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(925, 6561, F9, 7) (dual of [6561, 6536, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(935, 6572, F9, 9) (dual of [6572, 6537, 10]-code), using Gilbert–Varšamov bound and bm = 935 > Vbs−1(k−1) = 1440 343176 662748 970740 437426 415897 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(935, 6571, F9, 10) (dual of [6571, 6536, 11]-code), using
- construction X with Varšamov bound [i] based on
(26, 36, 2417084)-Net in Base 9 — Upper bound on s
There is no (26, 36, 2417085)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 22528 416323 072257 902355 344144 648457 > 936 [i]